RayTriangle.h

// Jolt Physics Library (https://github.com/jrouwe/JoltPhysics)
// SPDX-FileCopyrightText: 2021 Jorrit Rouwe
// SPDX-License-Identifier: MIT

#pragma once

JPH_NAMESPACE_BEGIN

/// Intersect ray with triangle, returns closest point or FLT_MAX if no hit (branch less version)
/// Adapted from: http://en.wikipedia.org/wiki/M%C3%B6ller%E2%80%93Trumbore_intersection_algorithm
JPH_INLINE float RayTriangle(Vec3Arg inOrigin, Vec3Arg inDirection, Vec3Arg inV0, Vec3Arg inV1, Vec3Arg inV2)
{
	// Epsilon
	Vec3 epsilon = Vec3::sReplicate(1.0e-12f);

	// Zero & one
	Vec3 zero = Vec3::sZero();
	Vec3 one = Vec3::sOne();

	// Find vectors for two edges sharing inV0
	Vec3 e1 = inV1 - inV0;
	Vec3 e2 = inV2 - inV0;

	// Begin calculating determinant - also used to calculate u parameter
	Vec3 p = inDirection.Cross(e2);

	// if determinant is near zero, ray lies in plane of triangle
	Vec3 det = Vec3::sReplicate(e1.Dot(p));

	// Check if determinant is near zero
	UVec4 det_near_zero = Vec3::sLess(det.Abs(), epsilon);

	// When the determinant is near zero, set it to one to avoid dividing by zero
	det = Vec3::sSelect(det, Vec3::sOne(), det_near_zero);

	// Calculate distance from inV0 to ray origin
	Vec3 s = inOrigin - inV0;

	// Calculate u parameter
	Vec3 u = Vec3::sReplicate(s.Dot(p)) / det;

	// Prepare to test v parameter
	Vec3 q = s.Cross(e1);

	// Calculate v parameter
	Vec3 v = Vec3::sReplicate(inDirection.Dot(q)) / det;

	// Get intersection point
	Vec3 t = Vec3::sReplicate(e2.Dot(q)) / det;

	// Check if there is an intersection
	UVec4 no_intersection =
		UVec4::sOr
		(
			UVec4::sOr
			(
				UVec4::sOr
				(
					det_near_zero,
					Vec3::sLess(u, zero)
				),
				UVec4::sOr
				(
					Vec3::sLess(v, zero),
					Vec3::sGreater(u + v, one)
				)
			),
			Vec3::sLess(t, zero)
		);

	// Select intersection point or FLT_MAX based on if there is an intersection or not
	return Vec3::sSelect(t, Vec3::sReplicate(FLT_MAX), no_intersection).GetX();
}

/// Intersect ray with 4 triangles in SOA format, returns 4 vector of closest points or FLT_MAX if no hit (uses bit tricks to do less divisions)
JPH_INLINE Vec4 RayTriangle4(Vec3Arg inOrigin, Vec3Arg inDirection, Vec4Arg inV0X, Vec4Arg inV0Y, Vec4Arg inV0Z, Vec4Arg inV1X, Vec4Arg inV1Y, Vec4Arg inV1Z, Vec4Arg inV2X, Vec4Arg inV2Y, Vec4Arg inV2Z)
{
	// Epsilon
	Vec4 epsilon = Vec4::sReplicate(1.0e-12f);

	// Zero
	Vec4 zero = Vec4::sZero();

	// Find vectors for two edges sharing inV0
	Vec4 e1x = inV1X - inV0X;
	Vec4 e1y = inV1Y - inV0Y;
	Vec4 e1z = inV1Z - inV0Z;
	Vec4 e2x = inV2X - inV0X;
	Vec4 e2y = inV2Y - inV0Y;
	Vec4 e2z = inV2Z - inV0Z;

	// Get direction vector components
	Vec4 dx = inDirection.SplatX();
	Vec4 dy = inDirection.SplatY();
	Vec4 dz = inDirection.SplatZ();

	// Begin calculating determinant - also used to calculate u parameter
	Vec4 px = dy * e2z - dz * e2y;
	Vec4 py = dz * e2x - dx * e2z;
	Vec4 pz = dx * e2y - dy * e2x;

	// if determinant is near zero, ray lies in plane of triangle
	Vec4 det = e1x * px + e1y * py + e1z * pz;

	// Get sign bit for determinant and make positive
	Vec4 det_sign = Vec4::sAnd(det, UVec4::sReplicate(0x80000000).ReinterpretAsFloat());
	det = Vec4::sXor(det, det_sign);

	// Check which determinants are near zero
	UVec4 det_near_zero = Vec4::sLess(det, epsilon);

	// Set components of the determinant to 1 that are near zero to avoid dividing by zero
	det = Vec4::sSelect(det, Vec4::sOne(), det_near_zero);

	// Calculate distance from inV0 to ray origin
	Vec4 sx = inOrigin.SplatX() - inV0X;
	Vec4 sy = inOrigin.SplatY() - inV0Y;
	Vec4 sz = inOrigin.SplatZ() - inV0Z;

	// Calculate u parameter and flip sign if determinant was negative
	Vec4 u = Vec4::sXor(sx * px + sy * py + sz * pz, det_sign);

	// Prepare to test v parameter
	Vec4 qx = sy * e1z - sz * e1y;
	Vec4 qy = sz * e1x - sx * e1z;
	Vec4 qz = sx * e1y - sy * e1x;

	// Calculate v parameter and flip sign if determinant was negative
	Vec4 v = Vec4::sXor(dx * qx + dy * qy + dz * qz, det_sign);

	// Get intersection point and flip sign if determinant was negative
	Vec4 t = Vec4::sXor(e2x * qx + e2y * qy + e2z * qz, det_sign);

	// Check if there is an intersection
	UVec4 no_intersection =
		UVec4::sOr
		(
			UVec4::sOr
			(
				UVec4::sOr
				(
					det_near_zero,
					Vec4::sLess(u, zero)
				),
				UVec4::sOr
				(
					Vec4::sLess(v, zero),
					Vec4::sGreater(u + v, det)
				)
			),
			Vec4::sLess(t, zero)
		);

	// Select intersection point or FLT_MAX based on if there is an intersection or not
	return Vec4::sSelect(t / det, Vec4::sReplicate(FLT_MAX), no_intersection);
}

JPH_NAMESPACE_END